Collaborative and geometric multi-kernel learning for multi-class classification. (March 2020) - Wang, Zhe; Zhu, Zonghai; Li, Dongdong
Highlights: CGMKL realizes the multi-class classification under the MEKL framework through combining the softmax function and MEKL. By doing so, the MEKL enriches the expressions of sample and greatly improves the classification ability of the softmax function. CGMKL offers the complementary information between different kernel spaces by introducing a regularization term RU, which keeps consistency outputs of samples in different kernel spaces. By doing so, classifiers in different kernel spaces can learn from each other and keep collaborative working. CGMKL makes the output trend of data suit for classification through introducing a regularization term RG, which reduces the within-class distance of the outputs of samples. By doing so, the classification result exhibits a geometric feature. Abstract: The multi-class classification is the problem of classifying the sample into one of three or more classes. In this paper, we propose an algorithm named collaborative and geometric multi-kernel learning (CGMKL) to classify multi-class data into corresponding class directly. The CGMKL uses the Multiple Empirical Kernel Learning (MEKL) to map the sample into multiple kernel spaces, and then trains the softmax function in each kernel space. To realize the collaborative learning, one regularization term, which controls the consistent outputs of samples in different kernel spaces, provides the complementary information. Moreover, another regularization term exhibits the classification result with a geometric feature by reducing the within-class distance of the outputs of samples. Extensive Experiments on the multi-class data sets validate the effectiveness of the CGMKL.